Charmless $B_s\to VS$ Decays in PQCD Approach

Abstract

In this work, we investigate the $B_s\to VS$ decays in the perturbative QCD approach, where $V$ and $S$ denote the vector meson and scalar meson respectively. Based on the two-quark structure, considering two different scenarios for describing the scalar mesons, we calculate the branching fractions and the direct $CP$ asymmetries of all $B_s\to VS$ decays. Most branching fractions are predicted to be at $10^{-7}$ to $10^{-5}$, which could be measured in the LHCb and Belle-II experiments, especially for these color-allowed $B_s\to \kappa (800)(K_0^{\ast }(1430))K^{\ast }$ decays. It is found that the branching fractions of $B_s\to K_0^{\ast 0}(1430){\bar{K}}^{\ast 0}$ and $B_s\to K_0^{\ast +}(1430){\bar{K}}^{\ast -}$ are very sensitive to the scenarios, which can be used to determine whether $K_0^{\ast 0}(1430)$ belongs to the ground state or the first excited state, if the data were available. We also note that some decays have large direct $CP$ asymmetries, some of which are also sensitive to the scenarios, such as the $B_s\to a_0^{+}(1450)K^{\ast -}$ and the $B_s\to f_0(1500)K^{\ast 0}$ decays. Since the experimental measurements of $B_s\to VS$ decays are on the way, combined with the available data in the future, we expect the theoretical predictions will shed light on the structure of the scalar mesons.

Comments: 18 Pages, 3 Figures